---
title: "Slip-ring IM rotor current at 4% slip"
subject: "Electrical Machine"
chapter: 5
key: "semester_4/electrical_machine:im-slipring-rotor-current-4-percent-slip"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/im-slipring-rotor-current-4-percent-slip
site: BCT Engineering
---

# Slip-ring IM rotor current at 4% slip

Electrical Machine · Chapter 5: Three Phase Induction Machines

- Asked in: 2069 Bhadra
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/im-slipring-rotor-current-4-percent-slip
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-5

## Question

A 3-phase, slip-ring, induction motor with star-connected rotor has an induced e.m.f. of 120 volts between slip-rings at standstill with normal voltage applied to the stator. The rotor winding has resistance per phase of 0.3 Ohm and standstill leakage reactance per phase of 1.5 Ohm. Calculate the current/phase when running short-circuited with 4% slip.

## Short answer

Rotor standstill emf per phase = 120/√3 = 69.28 V. At 4% slip, rotor emf = 2.771 V, reactance = 0.06 Ω, impedance = √(0.3²+0.06²) = 0.3059 Ω. Rotor current = 2.771/0.3059 = 9.06 A per phase.

## Answer

**Given:** star-connected rotor; standstill emf between slip rings = 120 V; R₂ = 0.3 Ω/phase; standstill reactance X₂ = 1.5 Ω/phase; slip s = 0.04; rotor short-circuited.

#### Step 1: Rotor emf per phase at standstill
E₂ = 120/√3 = 69.28 V

#### Step 2: Quantities at 4 % slip
```text
 Rotor emf per phase  sE2 = 0.04 × 69.28 = 2.771 V
 Rotor reactance      sX2 = 0.04 × 1.5   = 0.06 ohm
 Rotor impedance |Z2r| = √(0.3² + 0.06²) = √0.0936 = 0.3059 ohm
```

#### Step 3: Rotor current
I₂ = sE₂ / |Z₂ᵣ| = 2.771 / 0.3059 = **9.06 A per phase**

Rotor power factor = R₂ / |Z₂ᵣ| = 0.3/0.3059 = 0.981 lagging.

**Answer: rotor current ≈ 9.06 A per phase (rotor frequency 0.04 × 50 = 2 Hz if the supply is 50 Hz).**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The emf between slip rings is 120 V for star rotor. What is E2 per phase?
   A. 120 V
   B. 69.28 V
   C. 207.8 V
   D. 40 V
   Answer: B. Phase = 120/sqrt(3) = 69.28 V. (Key point: Phase emf)

2. At 4 % slip which quantities scale with s?
   A. Emf and reactance, not resistance
   B. Resistance only
   C. Emf, resistance and reactance
   D. Reactance only
   Answer: A. Rotor emf and reactance are proportional to s; R2 = 0.3 ohm is unchanged. (Key point: Quantities at slip)

3. What is the rotor current per phase?
   A. 69.28/0.3 = 231 A
   B. 2.771/0.3059 = 9.06 A
   C. 2.771/0.3 = 9.24 A
   D. 69.28/0.3059 = 226 A
   Answer: B. I2 = sE2/sqrt(R2^2 + (sX2)^2) = 9.06 A. (Key point: Rotor current)

## Related in Electrical Machine

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